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In the context of the Continuum Damage Mechanics, dierent types of non-local formulations are discussed, i.e., non local integral models, and gradient models both of explicit and implicit type. A unifying approach is described, based on the introduction of the nonlocality constraint into the energy expression through a lagrangian multiplier. Therefore, the solving equations of the problems follow as stationarity conditions of the lagrangian functional. Finally, some numerical results for a 2D example are presented.